MASSAPEQUA PUBLIC SCHOOLS

Transcription

1 MASSAPEQUA PUBLIC SCHOOLS Mathematics SAT/ACT Prep Summer 2015 COMMITTEE MEMBERS Jessica Yandoli BOARD OF EDUCATION Jane Ryan President Maryanne Fisher Vice President Gary Baldinger Secretary Joseph LaBella Trustee Timothy Taylor Trustee ADMINISTRATION Lucille F. Iconis, Superintendent Alan C. Adcock, Deputy Superintendent Thomas Fasano, Ed.D., Assistant to the Superintendent for Curriculum & Instruction Robert Schilling, Executive Director Assessment, Student Data and Technology Services Diana Haanraadts, Asst. to the Superintendent for Instructional Support & General Administration Dina Maggiacomo, Executive Director for Human Resources & General Administration Jean Castelli, Executive Director of Special Education and Student Support Services 1

2 Course Description/Rationale This course is intended to prepare students for the SAT Reasoning exam and ACT exam. It will offer strategies and tactics to use in solving the various types of math questions. Courses of this type generally improve Math SAT scores, but any such improvement will vary with the individual student. Technology is integrated throughout the curriculum. The new SAT exam, beginning in March 2016, has a calculator and non calculator sections. When permitted, students may use graphing calculators or scientific calculators to investigate topics and practice with. The curriculum identifies students prior knowledge from past courses. Currently, there is no textbook. Key Words for Curriki SAT and ACT Prep 2

3 Table of Contents Course Description/Rationale Key Words for Curriki Common Core State Standards, Learning Standards, Key Ideas & Performance Indicators For Content Area Curriculum Aligned with Common Core State Standards, Key Ideas & Performance Indicators Unit 1 : Introduction to the Course Unit 2 : Problem Solving and Data Analysis Unit 3 : Additional Topics Unit 4 : Practice ACT #1 Unit 5 : Practice SAT #1 Unit 6 : Passport to Advanced Math Topics Unit 7 : The Heart of Algebra Topics Unit 8 : Practice ACT Test #2 Unit 9 : Practice SAT Test #2 Unit 10 : Conclusion to Course 3

4 Common Core State Standards, Learning Standards, Key Ideas & Performance Indicators For Content Area Standards for SAT Exam : Emphasis on multi step problems. Requires the use of geometry concepts and reasoning. Includes statistics topics such as sampling and inferring correlation and causation from a research method. Requires the use of trigonometry. The test covers all math practices, with an emphasis on problem solving, modeling, using appropriate tools strategically, and recognizing and using algebraic structure. The test is broken down into four types of questions : 1. Heart of Algebra, which focuses on the mastery of linear equations and systems. Heart of Algebra questions ask students to: Create, solve, or interpret a linear expression or equation in one variable that represents a context. The expression or equation will have rational coefficients, and multiple steps may be required to simplify the expression, simplify the equation, or solve for the variable in the equation. Create, solve, or interpret linear inequalities in one variable that represent a context. The inequality will have rational coefficients, and multiple steps may be required to simplify or solve for the variable. Build a linear function that models a linear relationship between two quantities. The student will describe a linear relationship that models a context using either an equation in two variables or function notation. The equation or function will have rational coefficients, and multiple steps may be required to build and simplify the equation or function. Create, solve, and interpret systems of linear inequalities in two variables. The student will analyze one or more constraints that exist between two variables by creating, solving, or interpreting an inequality in two variables or a system of inequalities in two variables to represent a context. Multiple steps may be required to create the inequality or system of inequalities or to determine whether a given point is in the solution set. Create, solve, and interpret systems of two linear equations in two variables. The student will analyze one or more constraints that exist between two variables by creating, solving, or 4

5 analyzing a system of linear equations to represent a context. The equations will have rational coefficients, and multiple steps may be required to simplify or solve the system. Algebraically solve linear equations (or inequalities) in one variable. The equation (or inequality) will have rational coefficients and may require multiple steps to solve for the variable; the equation may yield no solution, one solution, or infinitely many solutions. The student may also be asked to determine the value of a constant or coefficient for an equation with no solution or infinitely many solutions. Algebraically solve systems of two linear equations in two variables. The equations will have rational coefficients, and the system may yield no solution, one solution, or infinitely many solutions. The student may also be asked to determine the value of a constant or coefficient of an equation in which the system has no solution, one solution, or infinitely many solutions. Interpret the variables and constants in expressions for linear functions within the context presented. The student will make connections between a context and the linear equation that models the context and will identify or describe the real life meaning of a constant term, a variable, or a feature of the given equation. Understand connections between algebraic and graphical representations. The student will select a graph described by a given linear equation, select a linear equation that describes a given graph, determine the equation of a line given a verbal description of its graph, determine key features of the graph of a linear function from its equation, or determine how a graph may be affected by a change in its equation. 2. Problem Solving and Data Analysis, which is about being quantitatively literate. Problem Solving and Data Analysis questions ask students to: Use ratios, rates, proportional relationships, and scale drawings to solve single and multistep problems. The student will use a proportional relationship between two variables to solve a multistep problem to determine a ratio or rate; calculate a ratio or rate and then solve a multistep problem; or take a given ratio or rate and solve a multistep problem. Solve single and multistep problems involving percentages. The student will solve a multistep problem to determine a percentage; calculate a percentage and then solve a multistep problem; or take a given percentage and solve a multistep problem. Solve single and multistep problems involving measurement quantities, units, and unit 5

6 conversion. The student will solve a multistep problem to determine a unit rate; calculate a unit rate and then solve a multistep problem; solve a multistep problem to complete a unit conversion; solve a multistep problem to calculate density; or use the concept of density to solve a multistep problem. Given a scatterplot, use linear, quadratic, or exponential models to describe how the variables are related. The student will, given a scatterplot, select the equation of a line or curve of best fit; interpret the line in the context of the situation; or use the line or curve of best fit to make a prediction. Use the relationship between two variables to investigate key features of the graph. The student will make connections between the graphical representation of a relationship and properties of the graph by selecting the graph that represents the properties described, or using the graph to identify a value or set of values. Compare linear growth with exponential growth. The student will infer the connection between two variables given a context in order to determine what type of model fits best. Use two way tables to summarize categorical data and relative frequencies, and calculate conditional probability. The student will summarize categorical data or use categorical data to calculate conditional frequencies, conditional probabilities, association of variables, or independence of events. Make inferences about population parameters based on sample data. The student will estimate a population parameter given the results from a random sample of the population. The sample statistics may mention confidence intervals and measurement error that the student should understand and make use of, but need not calculate. Use statistics to investigate measures of center of data and analyze shape, center, and spread. The student will calculate measures of center and/or spread for a given set of data or use given statistics to compare two separate sets of data. The measures of center that may be calculated include mean, median, and mode, and the measures of spread that may be calculated include range. When comparing two data sets, the student may investigate mean, median, mode, range, and/or standard deviation. Evaluate reports to make inferences, justify conclusions, and determine appropriateness of data collection methods. The reports may consist of tables, graphs, or text summaries. 6

7 3. Passport to Advanced Math, which features questions that require the manipulation of complex equations. Passport to Advanced Math questions ask students to: Create a quadratic or exponential function or equation that models a context. The equation will have rational coefficients and may require multiple steps to simplify or solve the equation. Determine the most suitable form of an expression or equation to reveal a particular trait, given a context. Create equivalent expressions involving rational exponents and radicals, including simplifying or rewriting in other forms. Create an equivalent form of an algebraic expression by using structure and fluency with operations. Solve a quadratic equation having rational coefficients. The equation can be presented in a wide range of forms to reward attending to algebraic structure and can require manipulation in order to solve. Add, subtract, and multiply polynomial expressions and simplify the result. The expressions will have rational coefficients. Solve an equation in one variable that contains radicals or contains the variable in the denominator of a fraction. The equation will have rational coefficients, and the student may be required to identify when a resulting solution is extraneous. Solve a system of one linear equation and one quadratic equation. The equations will have rational coefficients. Rewrite simple rational expressions. Students will add, subtract, multiply, or divide two rational expressions or divide two polynomial expressions and simplify the result. The expressions will have rational coefficients. Interpret parts of nonlinear expressions in terms of their context. Students will make connections between a context and the nonlinear equation that models the context to identify or describe the real life meaning of a constant term, a variable, or a feature of the given equation. Understand the relationship between zeros and factors of polynomials, and use that knowledge to sketch graphs. Students will use properties of factorable polynomials to solve conceptual problems relating to zeros, such as determining whether an expression is a factor of 7

8 a polynomial based on other information provided. Understand a nonlinear relationship between two variables by making connections between their algebraic and graphical representations. The student will select a graph corresponding to a given nonlinear equation; interpret graphs in the context of solving systems of equations; select a nonlinear equation corresponding to a given graph; determine the equation of a curve given a verbal description of a graph; determine key features of the graph of a linear function from its equation; or determine the impact on a graph of a change in the defining equation. Use function notation, and interpret statements using function notation. The student will use function notation to solve conceptual problems related to transformations and compositions of functions. Use structure to isolate or identify a quantity of interest in an expression or isolate a quantity of interest in an equation. The student will rearrange an equation or formula to isolate a single variable or a quantity of interest. 4. Additional Topics in Math, which includes the geometric and trigonometric skills most relevant to college and career readiness. Additional Topics in Math questions ask students to: Solve problems using volume formulas. The student will use given information about figures, such as length of a side, area of a face, or volume of a solid, to calculate missing information. Any required volume formulas will be provided to students either on the formula sheet or within the question. Use trigonometric ratios and the Pythagorean theorem to solve applied problems involving right triangles. The student will use information about triangle side lengths or angles presented in a context to calculate missing information using the Pythagorean theorem and/or trigonometric ratios. Add, subtract, multiply, divide, and simplify complex numbers. Convert between degrees and radians and use radians to determine arc lengths; use trigonometric functions of radian measure. The student will convert between angle measures in degrees and radians in order to calculate arc lengths by recognizing the relationship between an angle measured in radians and an arc length, evaluating trigonometric functions of angles in radians. 8

9 Apply theorems about circles to find arc lengths, angle measures, chord lengths, and areas of sectors. The student will use given information about circles and lines to calculate missing values for radius, diameter, chord length, angle, arc, and sector area. Use concepts and theorems about congruence and similarity to solve problems about lines, angles, and triangles. The student will use theorems about triangles and intersecting lines to determine missing lengths and angle measures of triangles. The student may also be asked to provide a missing length or angle to satisfy a given theorem. Use the relationship between similarity, right triangles, and trigonometric ratios; use the relationship between sine and cosine of complementary angles. The student will use trigonometry and theorems about triangles and intersecting lines to determine missing lengths and angle measures of right triangles. The student may also be asked to provide a missing length or angle that would satisfy a given theorem. Create or use an equation in two variables to solve a problem about a circle in the coordinate plane. The student will create an equation or use properties of an equation of a circle to demonstrate or determine a property of the circle s graph. Standards for ACT Exam : Number and Quantity (N) N 201. Perform one operation computation with whole numbers and decimals N 202. Recognize equivalent fractions and fractions in lowest terms N 203. Locate positive rational numbers (expressed as whole numbers, fractions, numbers) on the number line decimals, and mixed N 301. Recognize one digit factors of a number N 302. Identify a digit s place value N 303. Locate rational numbers on the number line Note: A matrix as a representation of data is treated here as a basic table. N 401. Exhibit knowledge of elementary number concepts such as rounding, the ordering of decimals, pattern identification, primes, and greatest common factor N 402. Write positive powers of 10 by using exponents N403. Comprehend the concept of length on the number line, and find the distance between two points 9

10 N 404. Understand absolute value in terms of distance N405. Find the distance in the coordinate plane between two points with the same x coordinate or y coordinate N 406. Add two matrices that have whole number entries N 501. Order fractions N 502. Find and use the least common multiple N 503. Work with numerical factors N 504. Exhibit some knowledge of the complex numbers N 505. Add and subtract matrices that have integer entries N 601. Apply number properties involving prime factorization N 602. Apply number properties involving even/odd numbers and factors/multiples N 603. Apply number properties involving positive/negative numbers N 604. Apply the facts that pi is irrational and that the square root of an integer is rational only if that integer is a perfect square N 605. Apply properties of rational exponents N 606. Multiply two complex numbers N 607. Use relations involving addition, subtraction, and scalar multiplication of vectors and of matrices N 701. Analyze and draw conclusions based on number concepts N 702. Apply properties of rational numbers and the rational number system N 703. Apply properties of real numbers and the real number system, including properties of irrational numbers N 704. Apply properties of complex numbers and the complex number system N 705. Multiply matrices N706. Apply properties of matrices and properties of matrices as a number system Algebra (A) and Functions (F) AF 201. Solve problems in one or two steps using whole numbers and using decimals in the context of money A 201. Exhibit knowledge of basic expressions (e.g., identify an expression for a total as b + g ) 10

11 A 202. Solve equations in the form x + a = b, where a and b are whole numbers or decimals F 201. Extend a given pattern by a few terms for patterns that have a constant increase or decrease between terms AF 301. Solve routine one step arithmetic problems using positive rational numbers, such as single step percent AF 302. Solve some routine two step arithmetic problems AF 303. Relate a graph to a situation described qualitatively in terms of familiar properties such as before and after, increasing and decreasing, higher and lower AF 304. Apply a definition of an operation for whole numbers (e.g., a b = 3 a b ) A 301. Substitute whole numbers for unknown quantities to evaluate expressions A 302. Solve one step equations to get integer or decimal answers A 303. Combine like terms (e.g., 2 x + 5 x ) F 301. Extend a given pattern by a few terms for patterns that have a constant factor between terms AF 401. Solve routine two step or three step arithmetic problems involving concepts such as rate and proportion, tax added, percentage off, and estimating by using a given average value in place of actual values. AF 403. Relate a graph to a situation described in terms of a starting value and an additional amount per unit (e.g., unit cost, weekly growth) AF 402. Perform straightforward word to symbol translations A 401. Evaluate algebraic expressions by substituting integers for unknown quantities A 402. Add and subtract simple algebraic expressions A 403. Solve routine first degree equations A 404. Multiply two binomials A 405. Match simple inequalities with their graphs on the number line (e.g x > 3/5) A 406. Exhibit knowledge of slope F 401. Evaluate linear and quadratic functions, expressed in function notation, at integer values AF 501. Solve multistep arithmetic problems that involve planning or converting common derived units of measure (e.g., feet per second to miles per hour) 11

12 AF 502. Build functions and write expressions, equations, or inequalities with a single variable for common pre algebra settings (e.g., rate and distance problems and problems that can be solved by using proportions) AF 503. Match linear equations with their graphs in the coordinate plane A 501. Recognize that when numerical quantities are reported in real world contexts, the numbers are often rounded A 502. Solve real world problems by using first degree equations A 503. Solve first degree inequalities when the method does not involve reversing the inequality sign A 504. Match compound inequalities with their graphs on the number line (e.g., 10.5 < x 20.3) A 505. Add, subtract, and multiply polynomials A 506. Identify solutions to simple quadratic equations A 507. Solve quadratic equations in the form ( x + a )( x + b ) = 0, where a and b are numbers or variables A 508. Factor simple quadratics (e.g., the difference of squares and perfect square trinomials) A 509. Work with squares and square roots of numbers A 510. Work with cubes and cube roots of numbers A 511. Work with scientific notation A 512. Work problems involving positive integer exponents A 513. Determine when an expression is undefined A 514. Determine the slope of a line from an equation F 501. Evaluate polynomial functions, expressed in function notation, at integer values F 502. Find the next term in a sequence described recursively F 503. Build functions and use quantitative information to identify graphs for relations that are proportional or linear F 504. Attend to the difference between a function modeling a situation and the reality of the situation F 505. Understand the concept of a function as having a well defined output value at each valid input value F 506. Understand the concept of domain and range in terms of valid input and output, and in terms of function graphs F 507. Interpret statements that use function notation in terms of their context 12

13 F 508. Find the domain of polynomial functions and rational functions F 509. Find the range of polynomial functions F 510. Find where a rational function s graph has a vertical asymptote F 511. Use function notation for simple functions of two variables AF 601. Solve word problems containing several rates, proportions, or percentages AF 602. Build functions and write expressions, equations, and inequalities for common algebra settings (e.g., distance to a point on a curve and profit for variable cost and demand) AF 603. Interpret and use information from graphs in the coordinate plane AF 604. Given an equation or function, find an equation or function whose graph is a translation by a specified amount up or down A 601. Manipulate expressions and equations A 602. Solve linear inequalities when the method involves reversing the inequality sign A 603. Match linear inequalities with their graphs on the number line A 604. Solve systems of two linear equations A 605. Solve quadratic equations Solve absolute value equations F 601. Relate a graph to a situation described qualitatively in terms of faster change or slower change F 602. Build functions for relations that are inversely proportional F 603. Find a recursive expression for the general term in a sequence described recursively F 604. Evaluate composite functions at integer values AF 701. Solve complex arithmetic problems involving percent of increase or decrease or requiring integration of several concepts (e.g., using several ratios, comparing percentages, or comparing averages) AF 702. Build functions and write expressions, equations, and inequalities when the process requires planning and/or strategic manipulation AF 703. Analyze and draw conclusions based on properties of algebra and/or functions AF 704. Analyze and draw conclusions based on information from graphs in the coordinate plane AF 705. Identify characteristics of graphs based on a set of conditions or on a general equation such as y = ax 2 13

14 + c AF 706. Given an equation or function, find an equation or function whose graph is a translation by specified amounts in the horizontal and vertical directions A 701. Solve simple absolute value inequalities A 702. Match simple quadratic inequalities with their graphs on the number line A 703. Apply the remainder theorem for polynomials, that P ( a ) is the remainder when P ( x ) is divided by ( x a ) F 701. Compare actual values and the values of a modeling function to judge model fit and compare models F 702. Build functions for relations that are exponential F 703. Exhibit knowledge of geometric sequences F 704. Exhibit knowledge of unit circle trigonometry F 705. Match graphs of basic trigonometric functions with their equations F 706. Use trigonometric concepts and basic identities to solve problems F 707. Exhibit knowledge of logarithms F 708. Write an expression for the composite of two simple functions Geometry (G) G 201. Estimate the length of a line segment based on other lengths in a geometric figure G 202. Calculate the length of a line segment based on the lengths of other line segments that go in the same direction (e.g., overlapping line segments and parallel sides of polygons with only right angles) G 203. Perform common conversions of money and of length, weight, mass, and time within a measurement system (e.g., dollars to dimes, inches to feet, and hours to minutes) G 301. Exhibit some knowledge of the angles associated with parallel lines G302. Compute the perimeter of polygons when all side lengths are given G 303. Compute the area of rectangles when whole number dimensions are given G 304. Locate points in the first quadrant G401. Use properties of parallel lines to find the measure of an angle G 402. Exhibit knowledge of basic angle properties and special sums of angle measures (e.g., 90, 180, and 360 ) 14

15 G 403. Compute the area and perimeter of triangles and rectangles in simple problems G404. Find the length of the hypotenuse of a right triangle when only very simple computation is involved (e.g., and triangles) G 405. Use geometric formulas when all necessary information is given G 406. Locate points in the coordinate plane G407. Translate points up, down, left, and right in the coordinate plane G 501. Use several angle properties to find an unknown angle measure G502. Count the number of lines of symmetry of a geometric figure G 503. Use symmetry of isosceles triangles to find unknown side lengths or angle measures G 504. Recognize that real world measurements are typically imprecise and that an appropriate level of precision is related to the measuring device and procedure G 505. Compute the perimeter of simple composite geometric figures with unknown side lengths G 506. Compute the area of triangles and rectangles when one or more additional simple steps are required G 507. Compute the area and circumference of circles after identifying necessary information G 508. Given the length of two sides of a right triangle, find the third when the lengths are Pythagorean triples G 509. Express the sine, cosine, and tangent of an angle in a right triangle as a ratio of given side lengths G 510. Determine the slope of a line from points or a graph G 511. Find the midpoint of a line segment G 512. Findthecoordinatesofapointrotated180 around a given center point G 601. Use relationships involving area, perimeter, and volume of geometric figures to compute another measure (e.g., surface area for a cube of a given volume and simple geometric probability) G 602. Use the Pythagorean theorem G 603. Apply properties of , , similar, and congruent triangles G 604. Apply basic trigonometric ratios to solve right triangle problems G 605. Use the distance formula G 606. Use properties of parallel and perpendicular lines to determine an equation of a line or coordinates of a point 15

16 G 607. Find the coordinates of a point reflected across a vertical or horizontal line or across y = x G 608. Find the coordinates of a point rotated 90 about the origin G 609. Recognize special characteristics of parabolas and circles (e.g., the vertex of a parabola and the center or radius of a circle) G 701. Use relationships among angles, arcs, and distances in a circle G 702. Compute the area of composite geometric figures when planning and/or visualization is required G703. Use scale factors to determine the magnitude of a size change G 704. Analyze and draw conclusions based on a set of conditions G 705. Solve multistep geometry problems that involve integrating concepts, planning, and/or visualization Statistics and Probability (S) S 201. Calculate the average of a list of positive whole numbers S202. Extract one relevant number from a basic table or chart, and use it in a single computation S 301. Calculate the average of a list of numbers S 302. Calculate the average given the number of data values and the sum of the data values S 303. Read basic tables and charts S 304. Extract relevant data from a basic table or chart and use the data in a computation S 305. Use the relationship between the probability of an event and the probability of its complement S 401. Calculate the missing data value given the average and all data values but one S 402. Translate from one representation of data to another (e.g., a bar graph to a circle graph) S 403. Determine the probability of a simple event S 404. Describe events as combinations of other events (e.g., using and, or, and not ) S 405. Exhibit knowledge of simple counting techniques S 501. Calculate the average given the frequency counts of all the data values S 503. Compute straightforward probabilities for common situations S 504. Use Venn diagrams in counting 16

17 S 505. Recognize that when data summaries are reported in the real world, results are often rounded and must be interpreted as having appropriate precision S 506. Recognize that when a statistical model is used, model values typically differ from actual values S 601. Calculate or use a weighted average S 602. Interpret and use information from tables and charts, including two way frequency tables S 603. Apply counting techniques S 604. Compute a probability when the event and/or sample space are not given or obvious S 605. Recognize the concepts of conditional and joint probability expressed in real world contexts S 606. Recognize the concept of independence expressed in real world contexts S 701. Distinguish between mean, median, and mode for a list of numbers S 702. Analyze and draw conclusions based on information from tables and charts, including two way frequency tables S 703. Understand the role of randomization in surveys, experiments, and observational studies S 704. Exhibit knowledge of conditional and joint probability S 705. Recognize that part of the power of statistical modeling comes from looking at regularity in the differences between actual values and model values 17

18 Curriculum Aligned with Common Core State Standards, Key Ideas & Performance Indicators The SAT and ACT tests are now following the Common Core Standards. 18

19 Unit 1: Introduction to the Course Student Outcomes Students review material from previous courses. Students develop basic fractions skill that they use for complex fractions. Students make connections from the basic fraction skills to have a better understanding of complex fractions. Students perform mathematical operations without using a calculator. Content map/calendar Lesson 1: Intro Assessment (1 Day) Students will learn about the SAT and ACT exams. Students will students will take an Intro Assessment on a Google Form. This assessment is to test what the students already know and in order to help the teacher understand the students better. Lesson 2: Basic Fractions (1 Day) No Calculator used during lesson. Discuss basic mathematical notes on integers. Review material from previous math courses: factors, multiples, operations with integers, comparing fractions, simplifying fractions, and addition & subtraction fractions with like and unlike denominators Lesson 3: Complex Fractions (1 Day) Extend fractions by working with Complex Fractions. Complex fractions will contain only numbers, no variables. 19

20 Technology Component Intro Assessment is a Google Form. Assessment Intro Assessment 20

21 Unit 2: Problem Solving and Data Analysis Student Outcomes Students understand when fractions or proportions can be used to help solve mathematical real world examples. Students connect previous knowledge of ratios, rates, proportions, percents, and units to higher level examples. Students will understand the difference between ratio, rate, and proportion. Content map/calendar Lesson 1: Ratios, Rates, & Proportions (1 Day) Discuss what a ratio is and when to use a ratio. Discuss a rate and how it is different from a ratio. Determine when it is appropriate to use a ratio vs. rate. Using knowledge of ratios and rates to determine how to set up a proportion. Determine when to set up a proportion vs. a ratio or rate. Discuss the differences between ratios, rates, and proportions. Lesson 2: Percents (1 Day) Students use previous knowledge of percents and apply it to higher level percent examples. Understand the relationship between a percentage written as a fraction and a decimal. Explore different methods to use for percents. *Multiply percent as a decimal or set up a proportion. Students recognize when to find the percentage vs. when to find the part/whole. Lesson 3: Units (1 Day) Students use previous knowledge from math and science courses to convert units. 21

22 Students understand the relationship between different units. Students extend knowledge to converting more than one unit at a time. Technology Component Khan Academy and, when appropriate, calculator use. Assessment Students will be given informal assessments throughout the unit on Khan Academy. 22

23 Unit 3: Additional Topics Student Outcomes Students review material from previous course. Students understand how to determine the volume formula and how to use it. Students recall the Pythagorean Theorem and apply it to real world problems. Discuss angle relationships and how they apply to similar and congruent figures. Discuss Trigonometric functions, their relationships, and understand when to apply them. Students will understand the difference between radians and degrees. Discuss circle vocabulary. Use the circle vocabulary to calculate arc length. Use circle vocabulary to determine how find the area of a sector. Content map/calendar Lesson 1: Volume (1 Day) Students use previous knowledge from past math course to determine the volume of different figures. Students will understand how to determine the volume formula for different figures, even though a reference sheet will be provided for them on the exams. Lesson 2: Right Triangle Word Problems (1 Day) Discuss how to find the third sides of Right Triangles using Pythagorean Theorem. Draw diagrams based off of examples. Then apply a method for finding the missing factor. Lesson 3: Congruence and Similarity (1 Day) Review angle measures such as: right angle, acute angle, obtuse angle, straight angle, reflex angle, full circle, complementary angles, supplementary angles, and congruent angles. Understand an angle bisector. 23

24 Review intersecting lines and angles, such as: perpendicular lines, parallel lines, a pair of intersecting lines that are not perpendicular, and parallel lines cut by a transversal. Use knowledge about angles to understand how corresponding angles are congruent. Use previous knowledge about proportions when working with similar figures. Use knowledge about angles to understand how corresponding sides of similar figures are in proportion. Lesson 4: Right Triangle Trigonometry (1 Day) Review the Pythagorean Theorem. Discuss how to find the third sides of Special Right Triangles ( , ). Discuss Trigonometric functions and the acronym SOHCAHTOA. Use SOHCAHTOA to determine trigonometry ratios in right triangles. Use SOHCAHTOA to find a missing angle or a side of right triangles. Understand the relationship between the different trigonometric functions and when to use which. Lesson 5: Angles, Arc Length, and Trigonometry Functions (1 Day) Discuss radians. Understand the difference between radians and degrees. Using previous knowledge, understand how to convert between radians and degrees and vice versa. Briefly discuss arc length and how arc length is different than the angle measurement in radians. This will be discussed more in the next lesson. Lesson 6: Circle Theorems (1 Day) Using previous knowledge of circles, discuss the following vocabulary terms: circle, chord, radius, diameter, arc, sector, semicircle. 24

25 Revisit arc length from Day 5 and discuss how to calculate the arc length. Use previous knowledge to determine how to find the area of a circular sector. Lesson 7: Circle Equations (1 Day) Use previous knowledge of circle equations to write the equation of a circle and to determine the radius and center of a circle. Explore how the Pythagorean Theorem can be used to determine the equation of a circle. Lesson 8: Complex Numbers (1 Day) Discuss real numbers. Discuss imaginary numbers and how they differ from real numbers. Understand how to simplify imaginary numbers. Understand and recognize a pattern when an imaginary number is raised to different powers. Understand how to add and subtract complex numbers. Use previous knowledge of the Box Method to understand how to multiply binomial complex numbers. Technology Component Khan Academy and, when appropriate, calculator use. Assessment Students will be given informal assessments throughout the unit on Khan Academy. 25

26 Unit 4: Practice ACT #1 Student Outcomes Students review the ACT exam and understand the format of the test. Students perform mathematical operations with a calculator, when necessary. Students develop test taking skills for taking the ACT exam. Students work together to have a better understand of the material. Discuss any questions the students still have. Content map/calendar Lesson 1: Intro to ACT & ACT Practice Exam #1 (2 Days) Understand the ACT exam. Begin and Finish the practice ACT exam. Lesson 2: Go Over ACT Practice Exam #1 (2 Days) Students will work in groups to help each other with the questions they got wrong on the practice ACT exam. As a whole class, the teacher and students will go over any questions the students still had difficulty with. Technology Component When appropriate, calculator use. Assessment Practice ACT Exam #1 26

27 Unit 5: Practice SAT #1 Student Outcomes Students review the SAT exam and understand the format of the test. Students perform mathematical operations with a calculator, when permitted. Students develop test taking skills for taking the SAT exam. Students work together to have a better understand of the material. Discuss any questions the students still have. Content map/calendar Lesson 1: Intro to SAT & SAT Practice Test #1 Section 3 (1 Day) Understand the SAT exam. Begin and Finish the practice SAT exam Section 3. Lesson 2: Go over SAT Practice Test #1 Section 3 (1 Day) Students will work in groups to help each other with the questions they got wrong on the practice SAT exam Section 3. As a whole class, the teacher and students will go over any questions the students still had difficulty with. Lesson 3: SAT Practice Test #1 Section 4 (2 Days) Begin and Finish the practice SAT exam Section 4. Lesson 4: Go over SAT Practice Test #1 Section 4 (2 Days) Students will work in groups to help each other with the questions they got wrong on the practice SAT exam Section 4. As a whole class, the teacher and students will go over any questions the students still had difficulty with. 27

28 Technology Component When appropriate, calculator use. Assessment Practice SAT Exam #1 28

29 Unit 6: Passport to Advanced Math Topics Student Outcomes Students review material from earlier in this course and from previous courses. Students recall different factoring methods. Students recall adding and subtracting fractions. Discuss the relationship between radicals and exponents. Discuss how to solve equations with radicals and exponents. Use knowledge of combining like terms when add and subtract radicals. Students will review different operations with variables, such as Addition and Subtraction and Multiplication and Division, with polynomials. Content map/calendar Lesson 1: Solving Quadratic Equations (1 Day) Students will review types of factoring such as: Greatest Common Factor, Difference of Two Perfect Squares, and Trinomial Factoring (Where the a =1). Using the review of Trinomial Factoring, students will recall how solve a quadratic equation. Students will explain the difference between factoring and solving quadratics. Lesson 2: Radicals & Rational Exponents and Radicals & Rational Equations (1 Day) Students will review radicals and how to simplify radicals. Include simplifying variable radicands. Students will review how to add, subtract, multiply and divide radicals. Students will review exponents, how to expand exponents, and the inverse of exponents. Students will make connections between radicals and exponents. Discuss how to solve equations with radicals and exponents. 29

30 Lesson 3: Operations with Polynomials (1 Day) Students will review how to use different operations with variables, such as Addition and Subtraction and Multiplication and Division. Students will discuss how to simplify like terms. Using the previous knowledge, students will connect how to use the same operations with polynomials. Lesson 4: Operations with Rational Expressions (1 Day) Review factoring, adding and subtracting fractions Use different operations with variables, such as Addition and Subtraction and Multiplication and Division. Technology Component Khan Academy and, when appropriate, calculator use. Assessment Students will be given informal assessments throughout the unit on Khan Academy. Unit 7: The Heart of Algebra Topics 30

31 Student Outcomes Students solve linear systems algebraically and graphically. Students develop facility with graphical interpretations of systems of equations and the meaning of their solutions on those graphs. Students understand how to solve and graph a system consisting of two linear equations and two inequality systems. Students use previous knowledge when working with linear systems. Content map/calendar Lesson 1: Solving Linear Equations & Interpreting Linear Functions (1 Day) Recall a Linear Equations. Students solve Linear Equation algebraically. Students understand and explain how to interpret Linear Functions. Lesson 2: Linear Equation Word Problems & Linear Function Word Problems (1 Day) Students discuss how to extract information from word problems to write Linear Equations. Students write Linear Equations and solve. Lesson 3: Graphing Linear Equations & Solving Systems of Linear Equations (1 Day) Recall how to graph Linear Functions. Students graph two Linear Equations and find the point of intersection. Students understand the relationship of solving Linear Equations by graphing and solving algebraically. Lesson 4: Linear Inequality Word Problems & Systems of Linear Inequalities (1 Day) Discuss differences between a Linear Equation and Linear Inequality. 31

32 Recall how to graph Linear Inequalities. Students graph two Linear Equations and find solution set or find a point in the solution set. Students write Linear Inequalities and solve algebraically. Students understand the relationship of solving Linear Equations by graphing and solving algebraically. Technology Component Khan Academy and, when appropriate, calculator use. Assessment Students will be given informal assessments throughout the unit on Khan Academy. 32

33 Unit 8: Practice ACT Test #2 Student Outcomes Students review the ACT exam and understand the format of the test. Students perform mathematical operations with a calculator, when necessary. Students develop test taking skills for taking the ACT exam. Students work together to have a better understand of the material. Discuss any questions the students still have. Content map/calendar Lesson 1: Intro to ACT & ACT Practice Exam #2 (2 Days) Understand the ACT exam. Begin and Finish the practice ACT exam. Lesson 2: Go Over ACT Practice Exam #2 (1 2 Days) Students will work in groups to help each other with the questions they got wrong on the practice ACT exam. As a whole class, the teacher and students will go over any questions the students still had difficulty with. Technology Component When appropriate, calculator use. Assessment Practice ACT Exam #2 33

34 Unit 9: Practice SAT Test #2 Student Outcomes Students review the SAT exam and understand the format of the test. Students perform mathematical operations with a calculator, when permitted. Students develop test taking skills for taking the SAT exam. Students work together to have a better understand of the material. Discuss any questions the students still have. Content map/calendar Lesson 1: Intro to SAT & SAT Practice Test #1 Section 3 (1 Day) Understand the SAT exam. Begin and Finish the practice SAT exam Section 3. Lesson 2: Go over SAT Practice Test #1 Section 3 (1 Day) Students will work in groups to help each other with the questions they got wrong on the practice SAT exam Section 3. As a whole class, the teacher and students will go over any questions the students still had difficulty with. Lesson 3: SAT Practice Test #1 Section 4 (2 Days) Begin and Finish the practice SAT exam Section 4. Lesson 4: Go over SAT Practice Test #1 Section 4 (2 Days) Students will work in groups to help each other with the questions they got wrong on the practice SAT exam Section 4. As a whole class, the teacher and students will go over any questions the students still had difficulty with. 34

35 Technology Component When appropriate, calculator use. Assessment Practice SAT Exam #2 35

36 Unit 10: Conclusion to Course Student Outcomes Students review the material from this course. Students perform mathematical operations with a calculator, when necessary. Students develop test taking skills. Collect data to determine the students growth from the introduction assessment. Discuss any questions the students still have. Content map/calendar Lesson 1: Closing Assessment (1 Day) Students will students will take a Closing Assessment on a Google Form. This assessment is to test what the students have learned throughout this course. Lesson 2: Go Over Closing Assessment (1 Day) Students will work in groups to help each other with the questions they got wrong on the Closing Assessment. As a whole class, the teacher and students will go over any questions the students still had difficulty with. Technology Component Google Form and when appropriate, calculator use. Assessment Closing Assessment. 36